Class Meeting 26

Class Meeting 26 - CHEN 3010 Applied Data Analysis Class...

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CHEN 3010 Applied Data Analysis Class Meeting #26 Thursday, Dec. 2nd Today's Topics Reading for next Tuesday: pages 351-366 Optional Homework #11 due Tuesday, Dec. 7 th or Wed 9 am Final Exams from last two years posted on the web site Experimental Design Center Points for Curvature Testing 2 k Design for k > 2 Response Surface Methods Center Composite Designs
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Adding Center Points to a Factorial Design ( a good thing to do ) Factor A A low A high B low B high (1) a b ab Experiments run at 0-levels of the factors Consider n c replicates Benefits of center points: assessing "curvature" providing an independent estimate of the error Factorial designs without center points assume linear effects (effect values (slopes) independent of factor level Center points allow for quadratic models such as 22 0 1 1 2 2 12 1 2 11 1 22 2 y x x xx x x ββ β = ++ + + + these terms capture curvature Factor B
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Example: Use of Center Points with k = 3 Problem 7-9, Page 395 3 k 2 n Treatment I A B C AB AC BC ABC 1 2 (1) 1 -1 -1 -1 1 1 1 -1 221 311 a 1 1 -1 -1 -1 -1 1 1 325 435 b 1 -1 1 -1 -1 1 -1 1 354 348 ab 1 1 1 -1 1 -1 -1 -1 552 472 c 1 -1 -1 1 1 -1 -1 1 440 453 ac 1 1 -1 1 -1 1 -1 -1 406 377 bc 1 -1 1 1 -1 -1 1 -1 605 500 abc 1 1 1 1 1 1 1 1 392 419 Effect Responses 4 replicates run at A=B=C=0 Responses: 425, 400, 437, 418 average of responses at ± 1: F y 413.1 = average of responses at 0: C y 420 = avg = 420, stdev = 15.5 If curvature is negligible, these two averages should be about the same. Alternately, with a large difference, curvature is
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This note was uploaded on 10/11/2011 for the course CHEN 3010 taught by Professor Kompala,dh during the Spring '08 term at Colorado.

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Class Meeting 26 - CHEN 3010 Applied Data Analysis Class...

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